What are the implications of an infinite large universe?

[SelfSim]

Georg Cantor initiated his theory of sets in order to provide a mathematical treatment of infinite sets. Thus the distinction between the finite and the infinite lies at the core of set theory. Certain foundationalists, the strict finitists, reject the existence of infinite sets and thus recommend a mathematics based solely on finite sets. (wikipedia)

But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in. (Aristotle, Physics, Book 3, Chapter 6)

Well, thank you for finally revealing your true purpose behind your demonstrations of that particular line of argument.

I do not agree that invoking Aristotlean philosophy acts as some kind of arbiter in this ... namely because, as I was demonstrating waayy back in this thread, your opening supposition: 'suppose that the infinite does not exist in any way' is entirely dependent on what you mean by 'exists'.

I know how we arrive at the meaning of that term .. and it doesn't invoke the nonsensical definition of some so-called 'Justified True Belief'. Mine is an objectively demonstrable way of arriving at what we mean by that term .. called the scientific method which has demonstrably evolved since Aristotle's way of thinking.

Mathematics is not metaphysics.

Irrelevant line of argument.

The issue was never sorted out back in Hilbert's day. The herd just moved on.

Fair enough .. its all about making sense and usefulness, as opposed to endless philosophical navel-gazing nonsense which leads nowhere.

 

[SelfSim]

You are stuck in an endless loop of inane comments.
For the umpteenth time it doesn't matter that real numbers and integers are finite numbers; you are not examining numbers as individual entities but in sets which can be finite or infinite.
What a load a rubbish.
Its called an infinite or endless loop for a reason when the loop counter doesn't stop and the program runs indefinitely which occurs when it attempts to count an infinite set.
So it's not only the mathematicians and physicists that have got it wrong but also the computer scientists.
This is classic Dunning Kruger stuff.

I think it was revealed that the line of argument is quite deliberate, and was already known to lead to the infinite regression problem.

Mathematics is on secure ground, as is science, in the face of such 'arguments' which lead nowhere (as is demonstrated by not having been resolved by philosophers for thousands(?) of years).

 

[klutedavid]

At first glance this seems rational but it is your error. Infinity is not a number like other numbers it is the symbol/word we use for endless things.

Thanks, 'Infinity is not a number like other numbers it is the symbol/word'. If infinity is a word what is it doing on a number line?

This is true, Infinity is the concept that we use to describe this largest integer. Again, it itself is not an integer, it is a descriptor of this largest number that you cannot put an integer value on because you could always add one more.

Make up your mind. Is infinity a number or not? I thought infinity was a concept, an idea. Not a numerical entity.

Yes a line of finite length is finite, but how many points are on that line?

A finite number because they can be counted.

You can keep on dividing the line in half forever

You did it again, your dividing that line in half an abstract number of times. Which is illogical. Here let me have a go. Let's divide that line in half by a ghost number of times. I did what you did, introduced an idea into the equation defined as a variable.

and you will never have a piece of that line that has 0 length. (as the line segments get smaller and smaller we can say that they are infinitesimally small.

I have no idea what 'infinitesimally small' means? Your a philosopher, not a mathematician.

How many fractions are in the series (1/2, 1/4, 1/8, 1/16.... meaning this pattern repeats endlessly. The fractions are all real numbers, but the answer to how many fractions are in the series is infinity.

You have corrupted that sequence with your philosophy.

What is Infinity?

No one has any idea. The concept is far beyond men and mice.

 

[klutedavid]

I think it was revealed that the line of argument is quite deliberate, and was already known to lead to the infinite regression problem.

Mathematics is on secure ground, as is science, in the face of such 'arguments' which lead nowhere (as is demonstrated by not having been resolved by philosophers for thousands(?) of years).

As with all disciplines there are divisions in the herd. Always, for and against. There are ten alternative theories for the Big Bang alone that I have seen.

I object when philosophical concepts are imposed onto number lines.

I object when counting numbers become uncountable numbers.

When words like 'infinity' which no one can understand, are employed into set theory.

I would not say that empiricism is on stable ground.

 

[SelfSim]

Thanks, 'Infinity is not a number like other numbers it is the symbol/word'. If infinity is a word what is it doing on a number line? Make up your mind. Is infinity a number or not? I thought infinity was a concept, an idea. Not a numerical entity.

Correct .. they're all demonstrably, concepts, including 'what numerical entities really are'.

The concept is far beyond men and mice.

Which is a totally nonsensical conclusion to arrive at, given that we are demonstrably, (objectively), discussing its existence in both science and math .. along with many, many other mathematicians and scientists everyday, everywhere in the biosphere.

 

[klutedavid]

Correct .. they're all demonstrably, concepts, including 'what numerical entities really are'.

Which is a totally nonsensical conclusion to arrive at, given that we are demonstrably, (objectively), discussing its existence in both science and math .. along with many, many other mathematicians and scientists everyday, everywhere in the biosphere.

So you can comprehend two trillion galaxies, which is the current tally in Astronomy.

The concept of String Theory and multiple universes is straight forward for you.

The concept of a singularity of infinite density occupying no space is simple really.

Quantum entanglement was a problem for Einstein but not for you.

Dark Energy and Dark Matter are mentioned often but does anyone know what these are?

Scientists and mathematicians use terminology all the time, without really understanding the philosophical ramifications.

 

[SelfSim]

As with all disciplines there are divisions in the herd. Always, for and against. There are ten alternative theories for the Big Bang alone that I have seen.

Different minds think in different ways on the same topic .. (no real news there) .. but it still takes a mind to conceive what infinity means.

Oh .. and cosmological models are .. well .. models! Different models are conceived to examine the logical consequences (and test them) of distinctly dissimilar behaviours. They aren't about 'proving what must truly exist'.

I object when philosophical concepts are imposed onto number lines.

I object when counting numbers become uncountable numbers.

Object all you like .. I predict you will never undo math theory on the philosophical grounds of a justified true belief. Thinking has evolved way beyond that.

When words like 'infinity' which no one can understand, are employed into set theory.

Infinity is perfectly understood in set theory .. by mathematical and scientific thinkers.

I would not say that empiricism is on stable ground.

That doesn't matter really though, does it?

 

[SelfSim]

So you can comprehend two trillion galaxies, which is the current tally in Astronomy.

The concept of String Theory and multiple universes is straight forward for you.

The concept of a singularity of infinite density occupying no space is simple really.

Quantum entanglement was a problem for Einstein but not for you.

Dark Energy and Dark Matter are mentioned often but does anyone know what these are?

I'm trying .. Its making the effort .. and not giving up, that ultimately counts for me .. although I can see that you see 'what counts' there, differs from that.

Scientists and mathematicians use terminology all the time, without really understanding the philosophical ramifications.

.. and they make useful and practical contributions to our everyday lives .. (like the computer you're using right now, to propagate your own philosophies).

 

[Ponderous Curmudgeon]

Thanks, 'Infinity is not a number like other numbers it is the symbol/word'. If infinity is a word what is it doing on a number line?Make up your mind. Is infinity a number or not? I thought infinity was a concept, an idea. Not a numerical entity.A finite number because they can be counted.You did it again, your dividing that line in half an abstract number of times. Which is illogical. Here let me have a go. Let's divide that line in half by a ghost number of times. I did what you did, introduced an idea into the equation defined as a variable.
I have no idea what 'infinitesimally small' means? Your a philosopher, not a mathematician.You have corrupted that sequence with your philosophy.No one has any idea. The concept is far beyond men and mice.

This is just the arogant argument from ignorance, you have not learned how the concept of infinity is used in mathematics and since it does not succumb to your simplistic world view, you claim that everyone else is wrong. You are incorrectly using the term illogical for that which you do not understand as opposed to in violation of logical principles such as those used to develop the mathematics that we rely on every day.

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

 

[sjastro]

I think it was revealed that the line of argument is quite deliberate, and was already known to lead to the infinite regression problem.

Mathematics is on secure ground, as is science, in the face of such 'arguments' which lead nowhere (as is demonstrated by not having been resolved by philosophers for thousands(?) of years).

You know philosophy bores me to tears.
As a matter of interest while the focus of infinity in this thread has been based on real numbers, infinity also crops up in the extended complex plane.
Recall a complex number z =x + yi where i is the imaginary √-1 can be mapped onto the x and y axes which is the complex plane.
In this case the complex plane can be wrapped around a sphere by a stereographic projection where infinity is now a point at the north pole.

Infinity in the complex plane is a completely different animal and allows arithmetic operations that are not defined for real numbers.
Examples being; z + ∞ = ∞, z - ∞ = ∞, z/0 = ∞, z/∞ = 0, ∞/0 = ∞ and 0/∞ = 0.

The only operations that are not defined as for real numbers are 0/0 and ∞/∞.
A fascinating subject.

 

[Ponderous Curmudgeon]

You know philosophy bores me to tears.
As a matter of interest while the focus of infinity in this thread has been based on real numbers, infinity also crops up in the extended complex plane.
Recall a complex number z =x + yi where i is the imaginary √-1 can be mapped onto the x and y axes which is the complex plane.
In this case the complex plane can be wrapped around a sphere by a stereographic projection where infinity is now a point at the north pole.

Infinity in the complex plane is a completely different animal and allows arithmetic operations that are not defined for real numbers.
Examples being; z + ∞ = ∞, z - ∞ = ∞, z/0 = ∞, z/∞ = 0, ∞/0 = ∞ and 0/∞ = 0.

The only operations that are not defined as for real numbers are 0/0 and ∞/∞.
A fascinating subject.

Thanks for resuscitating the brain cells that were in danger of dying from this thread. I either just learned something new or something I forgot 40 years ago.

 

[SelfSim]

You know philosophy bores me to tears.

Yeah .. me too (except where it allows for consistent science).

As a matter of interest while the focus of infinity in this thread has been based on real numbers, infinity also crops up in the extended complex plane.
Recall a complex number z =x + yi where i is the imaginary √-1 can be mapped onto the x and y axes which is the complex plane.
In this case the complex plane can be wrapped around a sphere by a stereographic projection where infinity is now a point at the north pole.

Infinity in the complex plane is a completely different animal and allows arithmetic operations that are not defined for real numbers.
Examples being; z + ∞ = ∞, z - ∞ = ∞, z/0 = ∞, z/∞ = 0, ∞/0 = ∞ and 0/∞ = 0.

The only operations that are not defined as for real numbers are 0/0 and ∞/∞.
A fascinating subject.

Like @Ponderous .. I find that diagram strangely reminiscent .. and hence familiarly credible .. Hmm ..

 

[SkyWriting]

If the universe is infinite then anything possible is actual. I have two comments:

1. That must be right.
2. That cannot be right.

Pick a number...

My understanding is that it's not infinite becasue it hasn't grown that large yet. There is no logical boundary stopping it's growth because you'd have to surpass the speed of light to find the edge, and that's not a possibility.
I mean the edge could be just outside of the moons orbit and we'd have to pass the speed of light to "see the edge" which is not practical. Realty expands faster than what we could see.

 

[Bradskii]

My understanding is that it's not infinite becasue it hasn't grown that large yet. There is no logical boundary stopping it's growth because you'd have to surpass the speed of light to find the edge, and that's not a possibility.
I mean the edge could be just outside of the moons orbit and we'd have to pass the speed of light to "see the edge" which is not practical. Realty expands faster than what we could see.

I think that the general perception that people have about the big bang is that it was a point in space that exploded. Well, yeah. It's called a big bang so that's quite reasonable. And then you can find examples of cosmologists saying that at time x, the universe was as big as...a grapefruit. Which locks in this idea of a finite ball of everything gradually getting bigger. But that's not what happened.

At the moment of the big bang, space and time came into being everywhere. Not just in some small area which then expanded out like a balloon getting bigger. And the 'size' of the universe at any given time is the size of the observable universe. It's the same difficulty we have if you suggest that the universe will someday shrink. It might, but it won't shrink to a specific point in space. It shrinks everywhere.

We're simply not capable of picturing in our minds eye exactly what happened. So we're certainly incapable of imagining the difference between a finite and an infinite universe.

 

[SkyWriting]

I think that the general perception that people have about the big bang is that it was a point in space that exploded. Well, yeah. It's called a big bang so that's quite reasonable. And then you can find examples of cosmologists saying that at time x, the universe was as big as...a grapefruit. Which locks in this idea of a finite ball of everything gradually getting bigger. But that's not what happened.

At the moment of the big bang, space and time came into being everywhere. Not just in some small area which then expanded out like a balloon getting bigger. And the 'size' of the universe at any given time is the size of the observable universe. It's the same difficulty we have if you suggest that the universe will someday shrink. It might, but it won't shrink to a specific point in space. It shrinks everywhere.

We're simply not capable of picturing in our minds eye exactly what happened. So we're certainly incapable of imagining the difference between a finite and an infinite universe.

But I just covered it and so did you. Space expands(we imagine) but "The inside" remains infinite at all times because we don't have the option of being outside it.

 

[Bradskii]

But I just covered it and so did you. Space expands(we imagine) but "The inside" remains infinite at all times because we don't have the option of being outside it.

If by 'inside' you mean the observable universe, then that is always a finite distance. We can't get to the edge but it's a set distance at any time.

 

[SkyWriting]

If by 'inside' you mean the observable universe, then that is always a finite distance. We can't get to the edge but it's a set distance at any time.

There is no way to say it's a "set Distance" because:
- space is expanding
- the "edge" is not visible or measurable.

 

[SelfSim]

There is no way to say it's a "set Distance"

Why ... its only logical, my good fellow (person) ..

because:
- space is expanding
- the "edge" is not visible or measurable.

So how do we know those things if it isn't by way of a logical (and empirical)model?

 

[SkyWriting]

Why ... its only logical, my good fellow (person) ..
So how do we know those things if it isn't by way of a logical (and empirical)model?

We can assume of course. Philosophy.

 

[Bradskii]

There is no way to say it's a "set Distance" because:
- space is expanding
- the "edge" is not visible or measurable.

The current radius of the observable universe is about 46 billion light years (so I guess we can measure it). At some point it will be exactly 47 billion light years. That's pretty set as distances go. I'll admit that it won't be exactly that size for long and we won't know the exact time it gets there (we won't be here), but it will be that exact size.